The Whale Song Translation: A Voyage of Discovery To Neptune and Beyond

by Howard Steven Pines

  “For God’s sake, man, that’s fantastic!” Greg thrust his arms triumphantly into the air. “Do it now and replay the recording of Uber’s vocalizations of the ellipses. Seema, while we’re waiting, do you think your symbol synthesizer can be modified to broadcast three different frequency peaks at the same time?”

  “Like Dmitri said,” replied Seema, “we’d already planned for that option. Even though my program is restricted to synthesizing tone pairs, I have the option to generate two tone pairs at the same time by the superposition principle. If you only want three peaks, I’ll zero the output energy of the fourth peak.”

  “That’s brilliant, Seema!” exclaimed Dmitri. “I didn’t realize you’d finished that. You two are amazing.”

  “Okay, I’m ready,” announced Andrew. “I’m replaying Uber’s recording back into the Speakeasy program which is now set up to analyze and plot the first three peaks. They should be appearing on the Speakeasy display any second now. Look, there’s the first ellipse.”

  They waited silently for the time it took to plot all four of the ellipses.

  “Are you kidding me?” howled Greg.

  “Oh, my,” uttered McPinsky. “Is this what I think it is?”

  “Yes,” answered Dmitri, surprised that his mentor’s voice had quavered with such emotion.

  “What is it?” asked Mark.

  “Could you elaborate, Professor?” Melanie echoed.

  “It’s a sublimely succinct calling card,” answered McPinsky, “rendered in the universal language of mathematics and written by the acoustic hand of the Megapterans. This is a message for the ages, transcending the proverbial ‘take-me-to-your-leader’ cliché. In Carl Sagan’s book Contact, he postulated that the first confirmed radio communication from an ET civilization was mathematical—a repeating series of the first 261 prime numbers.”

  “It’s rather elementary, Watson,” interjected Greg, facing Dmitri. “I’m visualizing the acoustical mastery of the mathematical expression of three-dimensional geometric figures. Uber has independent control of the rotation of these figures in all three dimensions. These ellipses are rotated independently by forty-five degrees around each of the three x, y, and z axes of the 3D plot.”

  To make his point, Greg traced his fingers across the shapes on the screen, and Dmitri muttered, “Amazing.” The static figures not only appeared to be rotated clockwise relative to one another, but in the 3D perspective of the x,y,z coordinates, they also seemed to pivot into the depth of the screen as well.

  When the boat momentarily swayed, Dmitri clutched the back of Andrew’s chair. “This is the mathematical basis of inertial guidance systems such as gyroscopes and gyrocompasses.” In awe, Dmitri reached out and touched the figures on the monitor. “Could this be how they navigate?”

  Gorman spoke in a quieter tone now, as if mystified. “I never imagined this—”

  “What are they talking about, Mom?” asked Mark. “What did the whale say?”

  “Honey, it’s even difficult for me to understand, but I think the whales are drawing 3D pictures with their voices.”

  “Awesome!” exclaimed Mark.

  Melanie turned her attention to the researchers. “You know, for thousands of years, what we heard as grunting or barking sounds is really a language of mathematics. Humans have adapted the written language to express both the representational symbols of the alphabet and the pictorial symbols like the Chinese ideograms. Likewise, as I see it now, the humpbacks have adapted their voices to express both the primitive logical game symbols, and in the pictorial mode, the ideograms of geometric figures in 3D no less.”

  “So whaddya think now, Chris?” asked Lila.

  “This is way beyond my grasp,” replied Gorman. “I’m relying on Dmitri and Greg to interpret the meaning of these signals.”

  Uber’s vocalizations resumed. He blasted away, over and over. As the cabin groaned with his roars, the geometric figures danced on the screen.

  “His control is unbelievable!” shouted Greg. “He just keeps retracing the same rotated figures with perfect precision.”

  “Oh, my God,” uttered Dmitri. “Look, now he’s rotating in the reverse direction, first counterclockwise, then clockwise.”

  The whale’s booming voice finally ceased.

  “I think he’s waiting for an answer,” said Andrew.

  “Who are we to refuse,” remarked McPinsky. “Don’t you think we should engage him in a three-dimensional version of the game?”

  “That’s an intriguing idea, Professor,” replied Dmitri, rubbing his hands together in anticipation. “Seema, is your synthesizer ready to broadcast that extra tone we discussed?”

  “It’s all set up and ready to go. I’ve even incorporated it into the random-tone-generation program. You want me to start with that?”

  “Yes,” said Dmitri. “Fire it up and cross your fingers. Hopefully, we’ll see a response.”

  With the addition of the third tone, the sounds of Seema’s computer-synthesized game symbols had a richer quality. The Speakeasy translations of the first few, ring-shaped symbols appeared to float in the three-dimensional perspective of the Speakeasy display.

  “Works like a charm,” said Greg.

  “Now the game becomes all the more challenging,” said Dmitri. “In addition to forming boxes in all three dimensions, a higher-level goal is to complete as many cubes of eight vertices as possible.”

  “I remember the original Star Trek television series,” said McPinsky, “where Spock and Kirk played a futuristic version of three-dimensional chess. I never imagined I might witness such a match between humans and another earthly species.” Dmitri sensed a degree of anticipation in McPinsky’s voice that he’d never heard before.

  “Hey, Andrew,” replied Greg. “There’s still something fishy about the shapes of the ellipses in three dimensions. Can you give me a raw data printout of the power levels and the frequencies of the four peaks?”

  “Fishy!” Dmitri heard Mark repeat, and he saw the boy was smiling.

  “Sure enough,” replied Andrew. “You’ll see the printout appearing in a couple of minutes, right over there.” He pointed at the printer located on the adjacent desk.

  “What are you up to, Greg?” asked Dmitri.

  “I’m not sure yet. Give me a few minutes to do some calculations.”

  “Hey, guys,” said Andrew. “I’m hearing game symbol responses from Uber.”

  “Okay, Seema, get ready.” Dmitri tensed. “I’ll give you the 3D coordinates and you feed them into your synthesizer.”

  Lila rushed over to Andrew’s workstation as Uber’s first ring-shaped symbols appeared. “Look at the screen! You were right, Greg. He’s playing the game in three dimensions. God, can this be happening?”

  Dmitri slapped Greg on the shoulder. “You’re a genius, pal.”

  As before, Uber projected the loop-shaped acoustic game symbols left and right, up and down, onto the LCD display. Now, however, the researchers could see that the placement of the symbols also receded into the depth dimension of the 3D Speakeasy soundscape.

  The match magically unfolded before their eyes. The circular symbols appeared to levitate in the three-dimensional perspective of the x,y,z plot. Now that the game had been translated into a higher dimension, the Turing test, the ultimate gauge of intellectual aptitude, was being performed upon a stage of even richer complexity. As the game progressed, boxes were transformed into cubes. The scoreboard’s mounting tallies confirmed the undeniable truth that, despite all of his training, Dmitri’s mind was not nearly as adept as his cetacean counterpart’s at manipulating the rules of logic in the extra dimension. The transcendent breakthrough more than compensated for his humbling defeat.

  * * *

  Ensconced in the executive leather chair in his home office, Professor Theodosious McPinsky stared at the revelation painted upon his computer monitor—the Speakeasy rendition of Uber’s 3D game masterpiece.

  To celebrate the occasio
n, he uncorked a rare, vintage bottle of his father’s favorite Scotch whisky. He yearned to share this special moment, so he filled two tumblers and placed the second drink next to the framed photo perched upon the desk. Then he raised his glass and toasted the lovely woman in the photograph, who perpetually smiled back at him. Savoring the Laphroaig single malt, he gazed longingly into the eyes of his departed wife, Emma, his own eyes wet with tears.

  * * *

  Back in California, Richard Prescott lounged in his den’s plush Italian leather recliner, and enjoyed an after-dinner snifter of Armagnac. With each pleasurable sip, he measured the minutes with great anticipation, waiting for the phone call from Maui to confirm the demise of Dmitri’s dangerous experiment.

  THE LORDS OF SOUND

  Research in Paradise Control Room

  If he’d had a box of cigars, Dmitri would have shared them with his giddy colleagues. He could only compare his current euphoria to his cousin’s description of elation at the birth of her first child.

  After a quick soda and chips mini-celebration in the Research in Paradise control room, Dmitri decided it was time to get back to work. He sat down at Andrew’s workstation. “Professor, are you still there?” The momentary silence suggested the Skype session had been terminated. “Professor?”

  “I’m here, my boy, but I doubt if I’m still the same person.”

  “I think we all feel that way,” replied Dmitri. “What are you thinking at this moment?”

  “I’m thinking that the use of logic and mathematics is regarded as the universal litmus test of higher intelligence. That the whales could be so adept at modulating and analyzing sound, in the same fashion that we utilize pen and paper to express these abstract concepts, is mind-boggling. Even humans don’t usually play games of logic in three dimensions without the assistance of a computer. Yet for centuries we judged the whales by our own arrogant standards, looking for the external vestiges of civilization, and we found them wanting.”

  “Their songs were only a clue to something much bigger.” Dmitri chuckled. “Now we literally have to face the music. This is the paradigm shift we’d been hoping for. For so long!”

  “All the same, we shouldn’t be too critical of ourselves,” replied McPinsky thoughtfully. “We couldn’t have achieved this breakthrough without the cutting-edge technology of the Speakeasy system.”

  “Speakeasy is the interspecies communication bridge you’d long sought, Professor,” replied Dmitri, his tone devotional. “It’s as if Homo sapiens had to progress to a level worthy of engaging with a species as advanced as the Megapterans.”

  “Now, if we could only cross that bridge with a sense of humility and the emotional intelligence to deal with the impact of such a dialogue,” said Melanie, who had appeared next to him. “Hello, Professor.” She raised her voice. “I don’t believe we’ve formally met. I’m Melanie.”

  Despite the afternoon’s flurry of incredible events, Dmitri felt chagrined he’d not yet introduced these two significant people in his life to one another. “I’m sorry Professor, but—”

  “So this is the brainy woman with the beautiful voice,” interrupted McPinsky. “Pleased to meet you.”

  Dmitri was pleasantly surprised by their instant camaraderie. “You’re right, Professor. It was Melanie’s Speakeasy training of her students that made this discovery possible.” He gazed into her eyes.

  “Thank you, Melanie,” replied McPinsky.

  “You’re welcome, Professor, but I believe Dmitri deserves the lion’s share of the credit.” She smiled at him. “I never dreamed Speakeasy could become a universal translator between beings that image symbols of light and beings that image symbols of sound.”

  “I believe we’ve only scratched the surface of our potential for communicating with these creatures,” said McPinsky.

  “You’re more correct than you can even imagine, Professor!” said Greg.

  “You certainly are jubilant, Greg,” noted Dmitri.

  “Prepare yourselves,” exclaimed Greg, “because the discoveries just keep on coming. I might have confirmed something even more remarkable!”

  “How could it get any better?” asked Dmitri.

  “It could be exponentially better,” replied Greg. “I just finished number crunching the raw frequency data of Uber’s 3D, rotated ellipses. These are just rough calculations, mind you. There’s possibly much more here than meets the eye. This is way beyond the perception of our physical senses. We would need more precise calculations, however, to confirm my finding.”

  Greg produced the data printout from Andrew’s workstation as the team gathered around him.

  “Look at this table of numbers.” He traced a finger across the rows and down the columns on the printed page. “These four columns correspond to the energy measurements of the first four frequency peaks in Uber’s raw-data spectra. They confirm what I suspected.”

  Dmitri peered at the numbers. “The energy levels are all in the same ballpark.”

  “Correct,” replied Greg. “From a cursory inspection of the waterfall plots, it also struck me that the time-dependent variations of the energies of the four peaks looked uncorrelated. This is compelling evidence that the four frequencies were intended to convey independent information. Because Uber’s rotated ellipses in 3D space looked suspiciously shaped, I finally remembered that the geometric projection of a circle from three dimensions into two dimensions has the shape of a squashed ellipse.”

  “Oh, my God!” uttered McPinsky. “Dr. Bono, don’t tell me you confirmed the existence of a geometric plane curve in tetra space?”

  “That’s what my rough calculations suggest,” Greg replied with a grin.

  Dmitri’s mind reeled at the outpouring of exuberant laughter from the speakerphone. Until today, he’d never heard his mentor react so emotionally. “Greg, please speak English. The suspense is killing me.”

  “Analogous to the projection of the 3D circle into a 2D ellipse, a circle ‘drawn’ in the abstract, mathematical world of four dimensions is transformed into the shape of an ellipse when projected into three dimensions. Let me repeat—” Greg reiterated what he’d just said, slowly and methodically. “I therefore wrote a quickie program for analyzing the raw data from Andrew’s printout and confirmed that the four-peak data satisfies the equation of a circle in four dimensions. Uber literally and figuratively ‘drew’ the acoustic version of a circle in four-dimensional space rotated four times by forty-five-degrees. Unfortunately, the human brain and eye can only interpret the plot of such a geometric construction as a three-dimensional ellipse.”

  “You’re pretty certain of this?” asked McPinsky.

  “Somewhat certain, yes, but only for the limited amount of data I’ve analyzed so far. By selecting different sets of eight points from the circumference of the alleged four-dimensional circle, I generated corresponding sets of eight simultaneous equations. For each and every one of those sets of equations, the solution always converged to the same answer for the radius, the location of the center, and the tilt angles. That a living organism could create this audio sequence of four-dimensional concentric circles is extremely difficult. Actually, it’s practically impossible.”

  “How so?” asked Lila.

  “One way to simulate this procedure is with a sophisticated computer program,” Greg said. “You’d first need to generate the geometrical figure of a four-dimensional hypersphere, a sphere existing in more than three dimensions, from the complex equation that describes it. Then you’d have a plane intersect the 4D hypersphere exactly through its center and tilted at the precise angle. Then you’d need to repeat this three more times for the same forty-five-degree angles of rotation.” His flattened palm and clenched fist simulated the geometry lesson of a plane and a sphere in three dimensions.

  “Are you saying Uber’s brain is like a supercomputer?” replied Lila.

  “What he’s saying,” answered McPinsky, in reverential tones, “is that Uber’s brain could be cap
able of processing symbols of information in four dimensions. To achieve the inconceivable mastery of four-dimensional frequency modulation, they’d need to precisely coordinate four independent streams of acoustic information to generate and image the symbols. We humans spend our whole lives learning to speak and understand language using only two independent streams. The humpbacks might be doing something exponentially more complex.”

  “The humpback’s acoustic ideograms might inherently be four-dimensional constructs,” added Greg. “If so, they could both literally and figuratively think and express themselves in four dimensions.”

  Once again, Dmitri observed the dazed expressions upon the faces of his colleagues. He marveled at this stunning turn of events, remembering how he’d battled with Greg about the original whale-song research proposal. Now his friend was leading the way, challenging the team with previously unimaginable possibilities.

  Andrew finally broke the silence. “First we were overjoyed to discover they could play a game of logic in two dimensions. Then we were thrilled to realize they could kick our butts in 3D. Now we’re stupefied to realize we’d need to program a supercomputer to have any chance of competing with them in 4D.”

  “It would certainly be a humbling realization for humankind,” added McPinsky.

  “Who’s going to believe any of this?” added Seema. “I can barely believe it myself.”

  “It’s all still speculative,” cautioned Greg. “We need to do a more thorough analysis of the data we’ve collected and submit it for peer review.”

  “But no one can argue with the facts,” replied Dmitri, “and we have the data to prove it. Andrew, just make sure you transmit those files to Professor McPinsky.”

  “I can’t believe I’m actually saying this, Dmitri, but maybe it’s time to turn on the video projector,” said Gorman. “Let’s give Uber the chance to experience the multi-sensory feedback of his mental machinations. It’s our chance to return the gift of this discovery.”